A physical quantity $z$ depends on four observables $a,$ $b,$ $c$ and $d ,$ as $z =\frac{ a ^{2} b ^{\frac{2}{3}}}{\sqrt{ c } d ^{3}} .$ The percentage of error in the measurement of $a, b, c$ and $d$ are $2 \%, 1.5 \%, 4 \%$ and $2.5 \%$ respectively. The percentage of error in $z$ is$......\%$

In an experiment four quantities $a, b, c$ and $d $ are measured with percentage error $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows $P = \frac{{{a^3}{b^2}}}{{cd}}$. $ \%$ error in $P$ is ........ $\%$

Write a note on combination of error.

The length and breadth of a rectangle are $(5.7 \pm 0.1) cm$ and $(3.4 \pm 0.2) cm$, respectively. Calculate the area of rectangle with error limits.

A physical quantity is $A = P^2/Q^3.$ The percentage error in measurement of $P$ and $Q$ is $x$ and $y$ respectively. Maximum error in measurement of $A$ is

In order to determine the Young's Modulus of a wire of radius $0.2\, cm$ (measured using a scale of least count $=0.001\, cm )$ and length $1 \,m$ (measured using a scale of least count $=1\, mm$ ), a weight of mass $1\, kg$ (measured using a scale of least count $=1 \,g$ ) was hanged to get the elongation of $0.5\, cm$ (measured using a scale of least count $0.001\, cm$ ). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in $\%$)